Assume that all the prime numbers up to this imaginary maximum prime number were multiplied together.

2*3*5*7*11*13*.......*A

'A' being the largest prime number.

The result would be even as 2 is a prime number and any whole number multiplied by 2 will produce an even number.

Consider the following

(2*3*5*7*11*13*.....*A) + 1

This number must be an odd numjber as any even number with 1 added on must be an odd number.

If you were to divide this number by any combination of the prime factors that make it up, it would not produce a whole number as you would always be left with a remainder, due to the extra 1 added on. This proves that the product of (2*3*5*......*A) + 1 is a prime number.

(2*3*5*.....*A) +1 is also larger than A, the supposed largest prime number, therefore there cannot be a largest prime number.

Pursuing the discovery of the largest prime number is alike trying to find the largest number you can fit on a piece of paper. It is completely irrelevant and silly.

saying the largest prime number has been found is about as much good as saying the largest even number has been found.

I disagree; although we know there are is no finite number of primes, the distribution of prime numbers is still not completely understood. Reimann's Hyptothesis ("All non-trivial zeros of the zeta-function are real part one half." The hypothesis could not be fully explained here, and I don't fully understand it anyway. Prime Obsession by John Derbyshire is an introduction suited for anyone with a basic knowledge of mathematics, though you can expect, as I encountered, too many things with holes -- stating what is there but not why it is there. I picked up Edwards' Riemann's Zeta Function, which appears to be more in depth.) and Goldbach's Conjecture (Basically, every even number is the sum of two primes.). Of course most people with a highschool education have heard of Riemann. And I am hardly an expert on any subject within mathematics (though one day I hope to be), so I'm sure there are other Stormfronters who see way past me in this area.

I disagree; although we know there are is no finite number of primes, the distribution of prime numbers is still not completely understood. Reimann's Hyptothesis ("All non-trivial zeros of the zeta-function are real part one half." The hypothesis could not be fully explained here, and I don't fully understand it anyway. Prime Obsession by John Derbyshire is an introduction suited for anyone with a basic knowledge of mathematics, though you can expect, as I encountered, too many things with holes -- stating what is there but not why it is there. I picked up Edwards' Riemann's Zeta Function, which appears to be more in depth.) and Goldbach's Conjecture (Basically, every even number is the sum of two primes.). Of course most people with a highschool education have heard of Riemann. And I am hardly an expert on any subject within mathematics (though one day I hope to be), so I'm sure there are other Stormfronters who see way past me in this area.

and in what way does any of this have any bearing on the discovery of yet another very large prime?

the distribution of primes is still not well understood for the simple reason that there is no regular distribution, nor can there be (since all the regularities are handled by the compound numbers). so for instance we believe that there is no end of twin primes, yet we can't say where they can be found altho it's easy to say where they can't be found (by the venerable sieve).

as for goldbach's conjecture: if proved true, it would be a simple proof that there is no largest prime. i leave the demonstration to you.